论文信息 - On the Orbit Decomposition of Finite Quandles

On the Orbit Decomposition of Finite Quandles

We study the structure of finite quandles in terms of subquandles. Every finite quandle $Q$ decomposes in a natural way as a union of disjoint $Q$-complemented subquandles; this decomposition coincides with the usual orbit decomposition of $Q$. Conversely, the structure of a finite quandle with a given orbit decomposition is determined by its structure maps. We describe a procedure for finding all non-connected quandle structures on a disjoint union of subquandles.

Sam Nelson | Chau-Yim Wong

[1] J. Vo,et al. Matrices and finite biquandles , 2006, math/0601145.

[2] Sam Nelson,et al. Symbolic computation with finite biquandles , 2005, J. Symb. Comput..

[3] Pedro Lopes,et al. On Finite Racks and Quandles , 2004, math/0412487.

[4] Sam Nelson,et al. Matrices and Finite Quandles , 2004, math/0412417.

[5] M. Elhamdadi,et al. Cocycle knot invariants from quandle modules and generalized quandle homology , 2003, math/0306068.

[6] P. Lopes,et al. Quandles at Finite Temperatures II , 2002, math/0205053.

[7] Nicolas Andruskiewitsch,et al. From racks to pointed Hopf algebras , 2002, math/0202084.

[8] P. Etingof,et al. On rack cohomology , 2002, math/0201290.

[9] P. Lopes. Quandles at Finite Temperatures I , 2001, math/0105099.

[10] Masahico Saito,et al. Quandle cohomology and state-sum invariants of knotted curves and surfaces , 1999, math/9903135.

[11] H. Ryder. The structure of racks , 1993 .

[12] Roger Fenn,et al. RACKS AND LINKS IN CODIMENSION TWO , 1992 .

[13] David Joyce,et al. A classifying invariant of knots, the knot quandle , 1982 .